The Ohlson Clean Surplus Theory or OCS is an interesting valuation model developed in academia and published in 1995. For readers not familiar with it, this article is dedicated to you.

**A note about the model's name**

I've seen this model, or similar versions, go by other monikers - Clean Surplus Model, Feltham & Ohlson (F&O), Edwards-Bell-Ohlson (EBO), Abnormal Earnings Growth Model or the Residual Income Model. It's confusing. It's unfortunate a definitive name hasn't arisen. I call it the Ohlson Clean Surplus, or OSC because that's what I learned it as.

**Why should you care about this model?**

Because of its academic origins, it's generated and continues to generate high-quality, peer-reviewed testing. The results indicate that it is a good predictor of future stock value, particularly in a time horizon of about two to three years.

The model is forward looking and as such, it has to make an estimate about the future. In my opinion, the estimate is relatively benign - it isn't hard to do nor is it pivotal to the results. However, there are some arbitrary assumptions and you have to decide if they make sense. We'll discuss both of these later in the article.

It's garnered the respect and praise of people who make a living out of advancing the state of the art. Stanford Professor, William H. Beaver considers it to be "one of the most important research developments in the past ten years.".

**The Challenges**

Although the math isn't inherently difficult, there is a lot of it as well as a number of data points. It isn't a calculation that can work easily if you are constructing it manually. From a practical point of view, you'll need software that can collect the data and run the calculations. I recommend Invrs, it can create any model you want, including this one.

Personally I find it complicated, although I've been surprised to see it described otherwise. Perhaps you won't.

Sometimes mathematical operations give weird results. For example calculating the PE ratio for a company with no or negative earnings will result in a meaningless answer. The OCS is no different. I think it's wise to review the inputs of the model, especially if this happens to you.

Because it's a model, the OCS is a simplified version of the real world. You might use the model against a stock that violates too many of the model's reductive components and wind up with an incorrect intrinsic valuation. I discuss some fixes in the section on Solutions to Problems with the Model.

So please, weigh the benefits against the costs and if you're interested, read on!

**The Theory**

This is a pragmatic article, not a theoretical one, but understanding a bit about the what and why will help with the how.

The model starts with the premise that if *all* of the assets and liabilities of a company were measured at fair value and faithfully recorded on the balance sheet you would know its value. However in the real world, we record assets and liabilities at historical cost (with some exceptions) and we don't record everything. Companies develop assets like trade secrets, client lists, intellectual property and incur liabilities such has lease obligations or other commitments that don't hit the balance sheet.

These two elements - the gap between the true value and the recorded value and the off-balance sheets items - create what's called "goodwill", but this is different than the accounting concept of goodwill. Goodwill in accounting can only be recorded when you purchase a company and it's the difference between what you paid and the fair market value. The OCS refers to internally generated goodwill, which is not recognized in accounting. This goodwill can also be defined as the present value of future abnormal earnings.

The OCS says that the value of a firm is composed of the portion we can see from the balance sheet and that portion we can't see, but can calculate. It's sort of like the way astronomers are able to measure black-holes by studying the way they bend light, even though they can't directly observe them.

This is the relationship:

Firm Value*(t)* = Book Value*(t)* + Goodwill

Let's continue to break down this down.

**The Calculation**

Because of the relationship between goodwill and abnormal earnings, we can write the formula this way:

Firm Value*(t)* = Book Value*(t)* + sum of the present value of abnormal earnings.

Further defining the elements in the calculation:

Abnormal earnings = projected actual earnings - accretion of discount,

Projected actual earnings = ROE x opening book value,

Accretion of discount = cost of capital x opening book value.

Calculating the opening book value for each subsequent year is an iterative process which depends on the end-of-year book value of the previous year. It works as follows:

Book value*(t+1) *= book value*(t)* x [1 + (1 - dividend payout ratio) x ROE]

To calculate the present value, we need the cost of capital, also known as the firm's rate, which is defined by the capital asset pricing model (CAPM):

Firm's rate = risk free rate x (1 - beta) + beta x market return.

**The Data Points, The Estimate and the Assumptions**

To execute this formula we need the following pieces of information, all of which can be determined from the company's financial statements or market statistics:

- Book value
- ROE (return on equity)
- Dividend payout ratio
- Risk free rate
- Company beta.

The estimate we have to make is the market return. I generally use the long term rate of return for the S&P of 7%, but you can use whatever you think is appropriate. Some people use a premium over the risk free rate.

The arbitrary assumptions are the ROE and the dividend payout ratio. The model as I presented it uses values calculated from the most recent year's financial statements, but those aren't necessarily the right ones to use. You'll need to decide if that makes sense in your analysis. Instead, you might want to look at analyst estimates for future earnings and temper your ROE accordingly. You may wish to look closer into the dividend policy of the company to find an explicit or implicit payout ratio. Or you might look at the historical rates of both and see if there's a pattern or trend, or simply take an average growth rate.

**Solutions to Problems with the Model**

it's a warning sign if there is a big difference between the intrinsic and market value. I believe the market is fairly efficient and when the intrinsic price is roughly more than plus or minus 40% of the actual price it's more indicative of a problem with the model rather than an opportunity.

If you get a valuation that doesn't look right, the first step is to look at the model's inputs. Look for:

- Dividend payout ratio > ROE
- Negative ROE
- A cost of capital that looks too high or too low

If you see any of the above decide if they should be changed and change them. For example, a dividend payout ratio greater than the company's ROE probably won't exist long term. If you see a negative ROE, investigate the reasons. Unless the company is going bankrupt, it should be a temporary event. If the firm's rate seems too high or too low, see if you can find a competitor with a similar capital structure and use that or adjust your estimate on the market's return.

If you still aren't satisfied, you can check your results against another valuation model. A simple one like the PE if the company has earnings greater than zero or price to sales if it doesn't.

Finally, use other metrics in addition to the OCS. Personally I look at the quality of earnings as well as earnings and/or sales growth.

**The OCS in Action**

I ran this against Facebook (NASDAQ:FB), in the expectation there would be a significant difference between the price and the OCS value so we could look for reasons and solutions.

To begin, we need our data points. Note all data and calculations were run using Invrs, bur were checked against the 10-K filings. With the exception of minor rounding differences all numbers are correct.

Book Value/Share: $20.47

ROE: 17.05% (There's different ways to calculate this, I used Diluted EPS/Book value/share)

Dividend Payout Ratio: 0

Risk free rate: 0.89% (the three month t-bill rate)

Beta: 1.1062

When I presented the formula I showed the general principle first and then broke down the details. In actual practice, you have to calculate the details first.

Facebook's cost of capital is 7.65% using 7% as the market return (0.0089 x (1 - 1.1062) + 1.1062 x 0.07)

It's future book values are as follows:

BV*(2017) *= 20.47*(1+(1-0)*0.1705) = $23.96

BV(*2018*) = 23.96*(1+0.1705) = $28.04

BV(*2019*) = $32.82

BV(*2020*) = $38.42

BV(*2021*) = $44.97

BV(*2022*) = $52.64

The abnormal earnings (NYSEMKT:AE) for each year are:

AE*(2017)* = .1705*20.47-0.0765*20.47 = 1.92

AE*(2018)* = 23.96*(.1705-.0765) = 2.25

AE*(2019)* = 28.04*(.094) = 2.64

AE*(2020)* = 32.82*(.094) = 3.09

AE*(2021)* = 38.42*(.0.94) = 3.61

AE*(2022)* = 44.97*(.094) = 4.23

AE*(2023)* = 52.64*(.0.94) = 4.95

Taking the present value of the abnormal earnings:

PV AE*(2017) *= 1.92 / (1.0765) = 1.78

PV AE*(2018)* = 2.25 / (1.0765) ^ 2 = 1.94

PV AE*(2019)* = 2.64 / (1.0765) ^ 3 = 2.12

PV AE*(2020)* = 3.09 / (1.0765) ^ 4 = 2.30

PV AE*(2021)* = 3.61 / (1.0765) ^ 5 = 2.50

PV AE*(2022)* =4.23 / (1.0765) ^ 6 = 2.72

PV AE*(2023)* = 4.95 / (1.0765) ^ 7 = 2.95

The sum of the present value of the abnormal earnings is $16.31 and the intrinsic value of Facebook is $20.47 + 16.31 = $36.78.

Facebook is currently trading around $150, so there is a huge difference here. What could be the reason?

In my opinion, it's the ROE. It needs to factor in a growth rate. Everything else from the firm's rate to the dividend payout ratio remaining at zero seems reasonable to me.

**Choosing the Growth Rate**

Facebook's growth is astounding. It's growing its user base at a compound rate of 14%, but its sales and profit grow even faster. Sales growth has averaged over 50% per year and it's net income averages over 120% (both calculated over five years of data). It's just mind-boggling.

The ROE growth over the past five years has been volatile, with one year showing modest growth (2.4%), two years showing tremendous growth (107% and 3,440%) and another showing a decline (-16%), so there's no pattern. The average gives a huge number (883%) which would be a ridiculous growth rate over 7 years leading to an unrealistic terminal ROE.

A quick and dirty calculation with net income doubling each year and equity increasing by the amount of net income results in a ROE of 93% after seven years when you start at a ROE of 18%. A compound growth rate of 14% will achieve this growth.

Introducing a ROE growth factor of 14% gives us an intrinsic value of $302.

If we change the ROE growth factor to 11%, after 7 years the return on equity is 66%. A more tolerable number, but still very high relative to, well, pretty much everything, At 11% Facebook has an intrinsic value of $166.

At 10% ROE growth ROE is 59% and the intrinsic value is $138.

**Conclusions on the Model and the Facebook Analysis**

The purpose of this article was to introduce a powerful valuation model to those unfamiliar with it. I wanted to give you it's pros and cons, a method of constructing it, trouble shooting it and show that you can be creative when solving valuation issues that might arise.

The OCS can indicate whether the stock is under, over or fairly valued. The exact intrinsic value you get isn't as important as the relative relationship between it and the actual price.

When you use it, you need to be happy with the assumptions. I don't think they need to be perfect, but they should feel right to you.

This wasn't meant to be a complete critique of Facebook or even a final statement on whether or not it's fairly valued. I have to say, it's stunning growth numbers made me a bit curious...how would hold up against a quality of earnings analysis? It scored really well, but I'll leave that for another article.

**Disclosure:** I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.

**Additional disclosure: **I work at Invrs, the analysis tool mentioned in the article.